1) Which of the following points lies in quadrant IV?

2) The point at which the two coordinate axes meet is called the

3) A point $P(a, b)$ is such that $a < 0$, $b > 0$. In which quadrant does P lies?

4) Distance between the points $(m, -n)$ and $(-m, n)$ is

5) Degree of the polynomial $4x^4 + 0x^3 + 0x^5 + 5x + 7$ is

6) Which of the following algebraic expressions is a linear polynomial?

7) If the point $(3, 4)$ lies on the graph of the equation $3y = ax + 7$, the value of a is:

8) If you take on 8 debts of ₹ 4 you have

9) The number of rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ is

10) Which of the following is not a rational number?

11) Which of the following is irrational?

12) $(a + b)^2 – 4ab =$

13) The expression $a^3 – b^3 – 3ab(a – b)$ is the expansion of

14) A semicircular protractor has radius 7 cm. Its perimeter is

15) How many circle(s) can be constructed that pass through all 3 vertices of $\Delta PQR$?

16) The line joining the centre of a circle to the midpoint of a chord is always

17) The side of a triangle are 3 cm, 4 cm and 5 cm. The area of triangle will be

18) If the area of a circle is $64\pi\text{ cm}^2$ then its circumference is

Assertion Reason Questions:
For questions 19 & 20, choose correct answer from the following options:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

19) Assertion (A) : Point $A(-2, -6)$ lies in the III quadrant
Reason (R) : A point both of whose coordinates are negative lies in the III quadrant

20) Assertion (A) : $\pi$ is a rational Number.
Reason (R) : $\pi$ can not be expressed as the ratio of two integers.

21) Find the value of $x$ for which the distance between the points $A (x, 2)$ and $B (9, 8)$ is 10 units.

22 (a) Find the value of the polynomial $p(x) = 4 + x^3 – x + 2x^2$ at $x = 0$ and $x = -1$

22 (b) Simplify $\frac{6}{7} (\frac{4}{9} – \frac{3}{2})$ using the distributive property.

23) Find the value of a, if $10000a = (9985)^2 – (15)^2$

24) Prove that equal chords of a circle subtend equal angles at the centre.

25 (a) Find the area of an equilateral triangle whose sides are 4 cm each.

25 (b) Find the area of a sector of a circle with radius 7 cm if angle of sector is $60^\circ$

26) If $A(5, 2)$, $B(2, -2)$ and $C(-2, t)$ are the vertices of right-angled triangle with $\angle B = 90^\circ$ then find the value of $t$.

27) In a school garden, the length of a rectangular flower bed is five more than three times its width. If the perimeter of the flower bed is 40 m, find its dimensions.

28 (a) Convert the decimal number in form $\frac{p}{q}$ : $23.\overline{43}$

28 (b) Prove that $\sqrt{3}$ is irrational

29 (a) If $x = 3 – 2\sqrt{2}$ and $y = 3 + 2\sqrt{2}$, then find the value of $x^2 + y^2$

29 (b) Simplify the rational expressions: $\left(\frac{3x^2 – 18x + 24}{2x^2 – 6x – 8}\right)$

30) In the given figure, O is the centre of the circle, if $\angle BDC = 72^\circ$ find:
(i) $\angle BAC$
(ii) $\angle BOC$

31) A triangular park ABC in a colony has sides 26 m, 28 m and 30 m as shown in the figure. The residents want to lay grass over the entire park at a cost of Rs 25 per square metre. Find the total cost.

32) A gym charges a fixed admission fee together with a fixed monthly fee. The total amount y (in rupees) for x month is given by $y = 30x + 500$
(i) Make a table of value of y for $x = 0, 2, 4, 6$
(ii) Draw the graph of the relation on a graph paper
(iii) Using the graph or otherwise, find the amount payable for 12 months.

33 (a) (i) $\frac{x^2 – 9}{x^2 + 7x + 12} \times \frac{x^2 + 2x – 8}{x^2 – 5x + 6}$ where the denominators are not zero. (3)
(ii) Using a suitable identity evaluate $(98)^3$ (2)

33 (b) (i) Factorise: $8a^3 + 36a^2b + 54ab^2 + 27b^3$ and hence write the side of a cube whose volume is this expression. (3)
(ii) If $x + \frac{1}{x} = 5$ find the value of $\frac{x^2 + 1}{x^2}$ (2)

34 (a) In the given figure PQ is a diameter of a circle. If $\angle QPT = 60^\circ$, $\angle PQR = 65^\circ$, $\angle SPR = 25^\circ$ find the measure of:
(i) $\angle PQT$
(ii) $\angle QPS$
(iii) $\angle QSR$
(iv) $\angle PSR$

34 (b) In the given figure BD is a diameter of the circle. If $\angle DBC = 48^\circ$ then find:
(i) $\angle BDC$
(ii) $\angle BEC$
(iii) $\angle BAC$

35) The parallel sides of trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal each being 26 cm. Find the area of trapezium.

Case Study 1
36) A village panchayat maintains a circular pond of radius 14 m. A triangular rest area ABC with sides 9 m, 12 m and 15 m is planned besides it, as shown. Take $\pi = \frac{22}{7}$

(i) Find the circumference of the pond. (1)
(ii) Find the area of the triangular rest area ABC using Heron’s formula. (1)
(iii) Find the area of the circular pond. (2)

(iii) Fencing is to be put along the boundary of the pond at ₹ 60 per metre. Find the total cost of fencing.

Case Study – 2
37) Three STD booths are placed at A, B and C as shown in the figure and these are operated by persons with disabilities. These three booths are equidistant from each other.

Based on the above information, answer the following questions:
(i) Find the measure of $\angle BAC$
(ii) If $AB = 8\text{ cm}$ find the value of $(BC + CA)$
(iii) Find the measure of $\angle BOC$
(iv) Find the sum of $\angle OBC$ and $\angle OCB$

Case Study – 3
38) A mother is 23 years older than her daughter and the product of the present age of the mother and the daughter is 680.
Based on the above information, answer the following questions:
i) Obtain a quadratic equation representing the given situation
ii) Find the present age of daughter
iii) Find the present age of mother